Find the greatest possible number for which 20% of that number is less than 100.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 500
Note: The given answer is as per the official NTA Answer Key. However, the answer given by NTA appears to be incorrect: 20% of 500 is 100 itself, which is not less than 100, so the greatest number among the options that fits the question is 300, Option (3), as explained below. In NTA’s key, 100 has quietly become less than 100.
20% of a number is one-fifth of it, so the condition sets an upper limit on the number:
\(20\%\) of \(N=\displaystyle\frac{N}{5}\lt 100\)
\(N\lt 500\)
So the number must be less than 500; 500 itself is the limit and does not qualify.
Option (1) 500 — Correct as per NTA; however, 20% of 500 is 100, which is equal to 100, not less. It would fit only if the question said “not more than 100”.
Option (2) 200 — Incorrect. 20% of 200 is 40, less than 100, but 300 is a greater number that also fits.
Option (3) 300 — Should have been correct. 20% of 300 is 60, less than 100, and it is the greatest option below 500.
Option (4) 600 — Incorrect. 20% of 600 is 120, which is more than 100.